Technical Field
The present invention relates generally to information processing and, in particular, to an efficient back-projection operation using a precomputed table.
Description of the Related Art
Three-dimensional (3D) Cone-Beam Computed Tomography (CBCT) is one of the most important and computationally-intensive medical imaging applications.
In CBCT and other medical imaging applications, a projection image data set is used as an intermediate product in order to reconstruct, via back-projection, the three-dimensional, internal structure of an imaged subject (e.g., a part of a body, and so forth). The projection image data set is a series of projection images of the object that were acquired at different projection angles in an image plane situated opposite the projection origin.
Volume imaging is achieved by first acquiring a series of cone beam projections of the object, where the beam source moves along some trajectory around the object, and then reconstructing the object from these projections, using a computer that executes a reconstruction algorithm. The reconstructed image consists of a 3D array of volume elements, or voxels. The reconstructed image represents a discrete approximation to the spatial distribution of the x-ray attenuation coefficient within a 3D region of the object. The coordinates of the voxels with respect to a reference frame are precisely known.
The core operation of the CBCT is the back-projection operation, which maps each voxel in the 3D volume onto the (2D) projection image.
In back-projection, the voxel, whose 3D position is denoted by {x, y, z}, is projected onto the point {un, vn} in the projection image data as follows:un(x,y,z)=(a0x+a3y+a6z+a9)·wn(x,y,z)−1,vn(x,y,z)=(a1x+a4y+a7z+a10)·wn(x,y,z)−1,wn(x,y,z)=a2x+a5y+a8z+a11 where An is a transformation matrix determined by the radiation detector in a CBCT system, a0 through an are values in the transformation matrix, and wn denotes the angle of rotation of the beam source and the detector.
The intensity value at the point {un, vn}, namely {circumflex over (p)}n, is calculated from the intensity values pn at the surrounding four grid points by bi-linear interpolation as follows:{circumflex over (p)}n(un,vn)=(1−α)(1−β)pn(i,j)+α(1−β)pn(i+1,j)+(1−α)βpn(i,j+1)+αβpn(i+1,j+1),i=└un┘,j=└vn┘,α=un−└un┘,β=vn−└vn┘
However, the preceding operation performed during the back-projection operation is computationally expensive. Accordingly, there is a need for accelerating the back-projection operation (e.g., in CBCT and other medical imaging applications) by reducing the amount of computation required to project voxels onto a projection image.